Maybe the New Republic is simply struggling after the fall of the Galactic Empire? The Republic slowly and then quickly transitioned its governmental apparatus into becoming the Empire, ruled under extreme military bureaucracy for twenty years, then collapsed. A New Republic wouldn’t necessarily have recovered to anything like the strength of the old Republic in that time.
This is sort of my line of thinking. Ignoring whatever canon says and just describing on way I like to interpret it: The New Republic sphere of influence is not as wide as the Old Republic’s was. I imagine the many worlds in the outer rim and the fringes of the galaxy are likely rather isolated from Republic influence. The Republic even had limited reach in the prequels, since Anakin’s mother said that the Republic essentially didn’t exist on Tatooine, and by extension the Outer Rim. Plus, it is possible not all systems chose to rejoin the Republic after the fall of the Empire, choosing to remain independent. So I imagine the New Republic might be, at most half the size of the Old Republic. Maybe 3/4 after 30 years of peace.
I imagine that over the decades, a lot of the Republic’s focus has been on just stabilizing the core and mid rim. They’ve probably tried to regrow their borders by either A) improve relationships with independent systems to try and get them to join/rejoin the Republic, and B) support resistance movements within Imperial Remnant territories in order to help liberate them and bring them back into the fold of the Republic. Our Resistance from the sequel trilogy being just one movement in particular that happens to be active in the territories of the First Order.
But I think one good way to address the Republic’s absence from the narrative is to play up the mystery of the First Order. What I mean by that is that the Republic should not know the scale of their power. The idea that they might have a super weapon shouldn’t even be on their radar. I think Poe’s surprised reaction to the inside of one of their Star Destroyers is a good display of this idea. He is almost in awe, like he had no idea the extent of the First Order’s resources.
Plus, if the First Order isn’t directly threatening the New Republic, then it makes sense why their guard would be down until it was too late. It really just a matter of finding ways to play that idea up. Like going with a word like mysterious to describe the First Order, rather than evil or sinister. I mean, as soon as we see stormtroopers we’ll know that they’re evil, so a different adjective might be more useful in the crawl. So yeah, something like mysterious, secretive, elusive, etc.
A word like radical, militant, fanatical could also paint a more descriptive picture than just evil as well. Though it may not help downplay the threat they pose to the New Republic.